Question

The sum of first 10 terms of the arithmetic progression 34, 32, 30, .….. is

• A. 200
• B. 225
• C. 250
• D. 275

Answer 1

The Correct Option is C

1. The given arithmetic progression (A.P.) is:

34, 32, 30, . . .

2. The formula for the sum of the first \(n\) terms of an A.P. is:

\( S_n = \frac{n}{2} \cdot (2a_1 + (n-1) \cdot d) \)

Where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the number of terms.

3. Finding the common difference:

The common difference \( d \) is the difference between any two consecutive terms:

\( d = 32 - 34 = -2 \)

4. Finding the sum of the first 10 terms:

Substitute \( a_1 = 34 \), \( d = -2 \), and \( n = 10 \) into the sum formula:

\( S_{10} = \frac{10}{2} \cdot (2 \cdot 34 + (10-1) \cdot (-2)) \)

\( S_{10} = 5 \cdot (68 + 9 \cdot (-2)) \)

\( S_{10} = 5 \cdot (68 - 18) \)

\( S_{10} = 5 \cdot 50 \)

\( S_{10} = 250 \)